Suppose that on each play of a game, a gambler either wins 1 with probability p or loses 1 with probability 1–p (or q). The gambler keeps betting until she or he is either up a total of n or down a total of m. What is the probability the gambler will quit an overall winner? You must consider both cases when p = 0.5 and when p ≠ 0.5

Step-by-step explanation:

From the given information,

Considering both cases when p = 0.5 and when p ≠ 0.5

the probability that the gambler will quit an overall winner is:

where ;

N.k = n  and k  = m

Hence, the probability changes to:

is  p ≠ 0.5   and k/N =  is P = 0.5

step-by-step explanation:

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